They might be low-hanging fruit but two things immediately come to mind:

* As more of the small stuff is just proven for free, the more they can be used as a basis for other proofs. If you know something is true or false for certain, that can be a significant tailwind for the much harder, much more important problems. Fermat's last theorem looks deceptively simple and invited many failed amateur attempts at solving it, but Wiles' proof drew on a diversity of seemingly-distant subfields within mathematics that were better understood.

* What are aspiring math Phd's supposed to do, now that the bar is much higher these days? The net effect of this appears to be that we'll see far fewer, but far more elite math Phd's, potentially discouraging many young people from the field.

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ndriscoll 2 hours ago | parent | next [-]

The bar for math PhDs already ruled out like 99.9% of the population, so I don't see it having much effect on discouraging people. The gap between even a bright student who takes AP calculus or whatever and someone studying e.g. spectral sequences is already incomprehensibly large. Like you literally could not even convey to a smart young person how far away they are from the boundary of today's understanding. I don't think I even have a reasonable sense with a math bachelor's!

People who get into math do it because they can't not do it.

	▲	ian-g an hour ago \| parent [-]
		I think it'll become increasingly important to have folks thinking about how to explain new math in a way that makes sense to your math bachelors students. And to your bright AP Calc students. If we can point ChatGPT at these problems and get eventual answers, that's awesome, but it'll still be important to figure out how to tell people why this matters in ways they understand.

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throwaway0123_5 4 hours ago | parent | prev | next [-]

> The net effect of this appears to be that we'll see far fewer, but far more elite math Phd's, potentially discouraging many young people from the field.

It seems plausible that the value of education will go down for the vast majority of fields and as a result less people will be getting degrees of all types.

Not a good outcome I think for humanity to be less educated, even if people are provided for when they can't get jobs... things like mathematical and scientific literacy, as well as history knowledge (which even STEM majors often receive via undergraduate degree breadth requirements), etc. I would expect strongly result in more informed and harder to deceive citizens.

	▲	CWuestefeld an hour ago \| parent [-]
		A large proportion of degrees awarded today are not useful for any practical application. But having a degree of some kind still serves as a signaling mechanism, demonstrating lots of things including the ability to "play the game". to follow instructions, and so forth.

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hgoel 3 hours ago | parent | prev | next [-]

I don't believe this is raising the bar for minting fresh PhDs.

We need to maintain perspective here, a PhD is essentially work done by a researcher at the least experienced, least skilled point of their career. Their primary goal is to demonstrate that they are capable of contributing to research.

They are not competing against AI to publish a counterexample to a known conjecture.

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chermi 4 hours ago | parent | prev | next [-]

Maybe masters will become more popular. I have no problem with bars being raised on PhDs, but it's crazy history that math may be the first one to have it raised (or brought back to old levels).

	▲	StableAlkyne 2 hours ago \| parent [-]
		IMO, I don't think this will raise the bar for PhDs. In every field of science, PhD student research is largely incremental. Very rarely is a thesis groundbreaking. The point of it is all is to function as an apprenticeship for that PhD student to become a scientist. Sometimes a particularly gifted or lucky one hits an important result, but that's rare and isn't the purpose.

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julianeon 4 hours ago | parent | prev | next [-]

Is the bar really higher? Those math PhD's can use GPT too; they benefit equally from AI assistance.

	▲	fn-mote an hour ago \| parent [-]
		This approach totally changes the game, in ways we are still discussing. The current consensus is that domain experts get the most out of using AI on problems. How will domain expertise develop when AI is doing the work? I’m not saying that there won’t be another approach that builds on the strengths of AI, but we have to look for that and develop it. There’s a lot to talk about.

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jauntywundrkind 2 hours ago | parent | prev [-]

Notably we have had very few conjectures proven true, so it doesn't feel like there is that widening base of established map to draw yet more proofs upon.